Large Language Models (LLMs) may hallucinate and generate fake information, despite pre-training on factual data. Inspired by the journalistic device of "according to sources", we propose according-to prompting: directing LLMs to ground responses against previously observed text. To quantify this grounding, we propose a novel evaluation metric (QUIP-Score) that measures the extent to which model-produced answers are directly found in underlying text corpora. We illustrate with experiments on three corpora (Wikipedia, PubMed, and the U.S. legal tax code) that these prompts improve grounding under our metrics, with the additional benefit of often improving end-task performance. Furthermore, prompts that ask the model to decrease grounding (or to ground to other corpora) indeed decrease QUIP-Score, indicating the ability of LLMs to increase or decrease grounded generations on request.